In the standard $(x,y)$ coordinate plane, what is the slope of the line that contains $(-2,-2)$ and has a $y$-intercept of $1$ ?

$-1$

$\dfrac{2}{3}$

$1$

$\dfrac{3}{2}$

$3$

Approach 1

Use the slope-intercept equation to find the slope:

$$ y=mx+b $$ $$ -2 = m(-2)+1 $$ $$ -2 = -2m+1 $$ $$ -3 = -2m $$ $$ m=\boxed{\frac{3}{2}} $$

Approach 2

Use the formula for slope:

$$ m = \frac{y_2-y_1}{x_2-x_1} $$

We are given a point $(-2,-2)$ and the $y$-intercept, $(0,1)$.

$$ m = \frac{1-(-2)}{0-(-2)} $$ $$ m=\boxed{\frac{3}{2}} $$